%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC422+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:41:10 PM UTC 2026
% Result : Theorem 1.93s 0.77s
% Output : CNFRefutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 4 unt; 4 def)
% Number of atoms : 238 ( 59 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 307 ( 111 ~; 102 |; 76 &)
% ( 4 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-4 aty)
% Number of variables : 162 ( 130 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( app(app(X4,cons(X2,nil)),X3) != W
| app(app(X3,cons(X2,nil)),X4) != X ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(app(X1,cons(Y,nil)),Z) = U
& app(app(Z,cons(Y,nil)),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| ~ neq(V,nil) ) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( app(app(X4,cons(X2,nil)),X3) != W
| app(app(X3,cons(X2,nil)),X4) != X ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(app(X1,cons(Y,nil)),Z) = U
& app(app(Z,cons(Y,nil)),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| ~ neq(V,nil) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| ( ? [X2] :
( ? [X3] :
( ? [X4] :
( app(app(X4,cons(X2,nil)),X3) = W
& app(app(X3,cons(X2,nil)),X4) = X
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(app(X1,cons(Y,nil)),Z) != U
| app(app(Z,cons(Y,nil)),X1) != V
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& neq(V,nil) ) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [U,V,W,X] :
( sP0_prd(X,W,V,U)
<=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( app(app(X4,cons(X2,nil)),X3) = W
& app(app(X3,cons(X2,nil)),X4) = X
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(app(X1,cons(Y,nil)),Z) != U
| app(app(Z,cons(Y,nil)),X1) != V
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& neq(V,nil) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| sP0_prd(X,W,V,U) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( ~ neq(sK50_skl,nil)
& neq(sK48_skl,nil) )
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) )
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& ssList(sK50_skl)
& ssList(sK49_skl)
& ssList(sK48_skl)
& ssList(sK47_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl)],[f417]) ).
fof(f423,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f424,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
( neq(sK48_skl,nil)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
( ~ neq(sK50_skl,nil)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
! [U,V,W,X] :
( ( ! [X2] :
( ! [X3] :
( ! [X4] :
( app(app(X4,cons(X2,nil)),X3) != W
| app(app(X3,cons(X2,nil)),X4) != X
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(app(X1,cons(Y,nil)),Z) = U
& app(app(Z,cons(Y,nil)),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ( ( ? [X2] :
( ? [X3] :
( ? [X4] :
( app(app(X4,cons(X2,nil)),X3) = W
& app(app(X3,cons(X2,nil)),X4) = X
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(app(X1,cons(Y,nil)),Z) != U
| app(app(Z,cons(Y,nil)),X1) != V
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
( ! [U,V,W,X] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( app(app(X4,cons(X2,nil)),X3) != W
| app(app(X3,cons(X2,nil)),X4) != X
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(app(X1,cons(Y,nil)),Z) = U
& app(app(Z,cons(Y,nil)),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( ? [X2] :
( ? [X3] :
( ? [X4] :
( app(app(X4,cons(X2,nil)),X3) = W
& app(app(X3,cons(X2,nil)),X4) = X
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(app(X1,cons(Y,nil)),Z) != U
| app(app(Z,cons(Y,nil)),X1) != V
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(miniscoping,[status(thm)],[f427]) ).
fof(f429,plain,
( ! [U,V,W,X] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( app(app(X4,cons(X2,nil)),X3) != W
| app(app(X3,cons(X2,nil)),X4) != X
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ( app(app(sK56_skl(X,W,V,U),cons(sK54_skl(X,W,V,U),nil)),sK55_skl(X,W,V,U)) = U
& app(app(sK55_skl(X,W,V,U),cons(sK54_skl(X,W,V,U),nil)),sK56_skl(X,W,V,U)) = V
& ssList(sK56_skl(X,W,V,U))
& ssList(sK55_skl(X,W,V,U))
& ssItem(sK54_skl(X,W,V,U)) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( app(app(sK53_skl(X,W,V,U),cons(sK51_skl(X,W,V,U),nil)),sK52_skl(X,W,V,U)) = W
& app(app(sK52_skl(X,W,V,U),cons(sK51_skl(X,W,V,U),nil)),sK53_skl(X,W,V,U)) = X
& ssList(sK53_skl(X,W,V,U))
& ssList(sK52_skl(X,W,V,U))
& ssItem(sK51_skl(X,W,V,U))
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(app(X1,cons(Y,nil)),Z) != U
| app(app(Z,cons(Y,nil)),X1) != V
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51_skl,sK52_skl,sK53_skl,sK54_skl,sK55_skl,sK56_skl]),skolemize(X2,sK51_skl(X,W,V,U)),skolemize(X3,sK52_skl(X,W,V,U)),skolemize(X4,sK53_skl(X,W,V,U)),skolemize(Y,sK54_skl(X,W,V,U)),skolemize(Z,sK55_skl(X,W,V,U)),skolemize(X1,sK56_skl(X,W,V,U))],[f428]) ).
fof(f431,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( app(app(X6,cons(X4,nil)),X5) != X3
| app(app(X5,cons(X4,nil)),X6) != X2
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f432,plain,
! [X0,X1,X2,X3] :
( ssItem(sK51_skl(X0,X1,X2,X3))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f433,plain,
! [X0,X1,X2,X3] :
( ssList(sK52_skl(X0,X1,X2,X3))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f434,plain,
! [X0,X1,X2,X3] :
( ssList(sK53_skl(X0,X1,X2,X3))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f435,plain,
! [X0,X1,X2,X3] :
( app(app(sK52_skl(X0,X1,X2,X3),cons(sK51_skl(X0,X1,X2,X3),nil)),sK53_skl(X0,X1,X2,X3)) = X0
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f436,plain,
! [X0,X1,X2,X3] :
( app(app(sK53_skl(X0,X1,X2,X3),cons(sK51_skl(X0,X1,X2,X3),nil)),sK52_skl(X0,X1,X2,X3)) = X1
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f442,definition,
( sQ0_spl
<=> sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,definition,
( sQ1_spl
<=> neq(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f446,plain,
( ~ sQ1_spl
| neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f448,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f425,f442,f445]) ).
fof(f449,definition,
( sQ2_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f451,plain,
( sQ2_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f442,f449]) ).
fof(f475,plain,
( ~ sQ0_spl
| sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f443]) ).
fof(f476,plain,
( ~ sQ0_spl
| sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f475]) ).
fof(f657,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( app(app(sK52_skl(X0,X1,X2,X3),cons(sK51_skl(X0,X1,X2,X3),nil)),sK53_skl(X0,X1,X2,X3)) != X6
| ~ ssList(sK53_skl(X0,X1,X2,X3))
| ~ ssList(sK52_skl(X0,X1,X2,X3))
| ~ ssItem(sK51_skl(X0,X1,X2,X3))
| ~ sP0_prd(X4,X5,X6,X1)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f436,f431]) ).
fof(f667,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( app(app(sK52_skl(X0,X1,X2,X3),cons(sK51_skl(X0,X1,X2,X3),nil)),sK53_skl(X0,X1,X2,X3)) != X6
| ~ ssList(sK53_skl(X0,X1,X2,X3))
| ~ ssList(sK52_skl(X0,X1,X2,X3))
| ~ sP0_prd(X4,X5,X6,X1)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f657,f432]) ).
fof(f1058,plain,
( sQ2_spl
| ~ neq(sK48_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f423,f451]) ).
fof(f2411,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( app(app(sK52_skl(X0,X1,X2,X3),cons(sK51_skl(X0,X1,X2,X3),nil)),sK53_skl(X0,X1,X2,X3)) != X6
| ~ ssList(sK53_skl(X0,X1,X2,X3))
| ~ sP0_prd(X4,X5,X6,X1)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f667,f433]) ).
fof(f2412,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sP0_prd(X0,X1,X2,X3)
| ~ ssList(sK53_skl(X0,X1,X2,X3))
| ~ sP0_prd(X4,X5,X0,X1)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f2411,f435]) ).
fof(f2434,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ ssList(sK53_skl(X0,X1,X2,X3))
| ~ sP0_prd(X4,X5,X0,X1)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(duplicate_literals_removal,[status(thm)],[f2412]) ).
fof(f2435,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sP0_prd(X4,X5,X0,X1)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f2434,f434]) ).
fof(f2524,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sP0_prd(sK48_skl,sK47_skl,X0,X1) ),
inference(resolution,[status(thm)],[f2435,f476]) ).
fof(f2532,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f476,f2524]) ).
fof(f2533,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f2532]) ).
fof(f2534,plain,
( sQ2_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1058,f446]) ).
fof(f2535,plain,
( sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f2534]) ).
fof(f2536,plain,
$false,
inference(sat_refutation,[status(thm)],[f448,f452,f2533,f2535]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC422+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n001.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 08:28:58 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 1.93/0.77 % Refutation found
% 1.93/0.77 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.93/0.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.93/0.80 % Elapsed time: 0.362579 seconds
% 1.93/0.80 % CPU time: 2.481949 seconds
% 1.93/0.80 % Total memory used: 136.580 MB
% 1.93/0.80 % Net memory used: 134.462 MB
%------------------------------------------------------------------------------